论文标题
在恒定水平风中具有二次阻力的介质中的弹丸运动
Projectile motion in a medium with quadratic drag at constant horizontal wind
论文作者
论文摘要
研究了弹丸以与地平线角度倾斜的弹丸运动的经典问题。使用二次阻力定律考虑了空气电阻力。还考虑了风的作用，这被认为是恒定和水平的。弹丸速度大张方程用于说明风的效果。提出了针对运动主要变量（笛卡尔弹丸坐标和时间）的相对简单的分析近似值。所有获得的公式仅包含基本功能。所提出的公式是通用的，也就是说，它们可用于任何初始投掷条件。此外，它们在广泛的参数更改中具有可接受的准确性。举例说明了高尔夫球，网球和羽毛球的运动作为例子。计算结果显示了所提出的分析解决方案与数值解决方案之间的良好一致性。提出的分析公式对于所有经典问题的研究人员都有用。
A classic problem of the motion of a projectile thrown at an angle to the horizon is studied. Air resistance force is taken into account with the use of the quadratic resistance law. The action of the wind is also taken into account, which is considered constant and horizontal. The projectile velocity hodograph equation is used to account for the effect of wind. Comparatively simple analytical approximations are proposed for the main variables of motion (cartesian projectile coordinates and time). All obtained formulas contain only elementary functions. The proposed formulas are universal, that is, they can be used for any initial conditions of throwing. In addition, they have acceptable accuracy over a wide range of the change of parameters. The motion of a golf ball, a tennis ball and shuttlecock of badminton are presented as examples. The calculation results show good agreement between the proposed analytical solutions and numerical solutions. The proposed analytical formulas can be useful for all researchers of this classical problem.
